Hibs had struggled to create chances and saw top goalscorer Leigh Griffiths carried off on a stretcher after Hearts midfielder Darren Barr accidentally stood on his ankle.
But their fans did not care in the slightest that their win was far scrappier than Hearts' 5-1 Hampden triumph, or that their 83rd-minute winner came from a fortunate own goal, David Wotherspoon's late strike deflecting off Marius Zaliukas, as they celebrated their first derby victory in 13 matches.
Finding Arvydas Novikovas early appeared to be a key facet to John McGlynn's tactics, and Ryan Stevenson did so with a crossfield ball after two minutes that led to the first chance. The Lithuanian sent over a deep cross that found Callum Paterson but his header was blocked by the legs of Ben Williams.
The first booking came shortly afterwards for Kebin McHattie's body-check on Wotherspoon, which sparked some home pressure.
Jamie McDonald punched clear two inswinging free-kicks by Griffiths and Tom Taiwo shot over from 20 yards but it proved a false dawn for Hibs. Paterson was inches away from getting on the end of another Novikovas cross and Williams produced a good reaction stop after a glancing header from Zaliukas bounched off Hibs defender Paul Hanlon's chest and towards the top corner.
Hearts continued to find Novikovas in space down the left. The Lithuanian fired well wide when a cross would have been a better option, appearing to hurt his ankle in the process, and then sent over a deep centre that drifted past Williams and bounced off the outside of the post.
Novikovas failed to appear after the break with Andrew Driver taking his place and Hibs created the first chance of the half but Eoin Doyle just could not reach Wotherspoon's flick-on.
They suffered a huge blow in the 51st minute when top goalscorer Griffiths was carried off after failing to get up following his tangle with Barr. Ross Caldwell came on and Barr himself soon limped off with a less serious looking knock with Scott Robinson taking his place.
Doyle was close to another Wotherspoon delivery before being replaced by Ivan Sproule, while John Sutton came on for the visitors as both managers looked to end the stalemate.
A breakthrough looked unlikely until the 83rd minute. Paul Cairney switched the ball to Wotherspoon on the right wing after a Hearts attack broke down. The midfielder had Jorge Claros inside him but he decided to go past McHattie and unleash a shot, which tooka heavy deflection off Zaliukas and flew over MacDonald and into the far corner.
Hearts threw men forward in a bid to hold on to their trophy but they could only create one half chance which Paterson fired over from 20 yards.